Markdown is good if you want simplicity that lets you do headings, emphasis and bold, and gets out of your way. I write fiction in Markdown.
AsciiDoc is good if you want structured documents. I would use it to write a technical manual.
Maybe a problem with AsciiDoc is that its name is scary. By the name "ascii" it seems to imply that there is a specific markup for typing non-ascii stuff, instead of simply typing the regular unicode characters (in whatever encoding).
Asciidoc is much more complex and so we only have 2 implementations around (a2x, asciidoctor).
Git, in the category of DVCS, is another example.
(although I'd argue that git's success stems from not pinning down the workflow early on, like competing DVCS did).
Exactly. For me the name "ASCII" feels like it is for older UNIX-era system experts.
The name might use to be fancy considering its initial version came out in 2002 (before markdown), but it became an unfortunate name.
For this reason, I'm using a blogging system (Pelican) that supports all of them (including Pythons Markdown extensions). I'm completely free to apply the best suiting variant to the topics requirements.